Showing papers on "Coherent states in mathematical physics published in 2015"
TL;DR: In this paper, the authors show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement.
Abstract: Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes.
41 citations
TL;DR: In this article, the authors describe coherent states for a physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential.
22 citations
TL;DR: In this paper, it was shown that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables, which is a property of coherent states.
Abstract: Coherent states provide a natural connection of quantum systems to their classical limit and are employed in various fields of physics. Here we derive general systematic expansions, with respect to quantum parameters, of expectation values of products of arbitrary operators within both oscillator coherent states and SU(2) coherent states. In particular, we generally prove that the energy fluctuations of an arbitrary Hamiltonian are in leading order entirely due to the time dependence of the classical variables. These results add to the list of well-known properties of coherent states and are applied here to the Lipkin-Meshkov-Glick model, the Dicke model, and to coherent intertwiners in spin networks as considered in loop quantum gravity.
17 citations
TL;DR: In this paper, the diagonal ordering operation technique (DOOT) was proposed to integrate the creation and annihilation operators of the harmonic oscillator coherent states, which has proved to be very fruitful for different operator identities and applications in quantum optics.
Abstract: The technique regarding the integration within a normally ordered product of operators, which refers to the creation and annihilation operators of the harmonic oscillator coherent states, has proved to be very fruitful for different operator identities and applications in quantum optics. In this paper we propose a generalization of this technique by introducing a new operatorial approach—the diagonal ordering operation technique (DOOT)—regarding the calculations connected with the normally ordered product of generalized creation and annihilation operators that generate the generalized hypergeometric coherent states. We have pointed out a number of properties of these coherent states, including the case of mixed (thermal) states. At the same time, by particularizing the obtained results to the one-dimensional harmonic and pseudoharmonic oscillators, we get the well-known results achieved through other methods in the corresponding coherent states representation.
15 citations
TL;DR: In this paper, the parity operator and nonlinear displacement-type operator were used to generate the superposition of two nonlinear coherent states and two-mode entangled nonlinear co-consistency states.
Abstract: In this paper, by using the parity operator as well as the nonlinear displacement-type operator, we define new operators which by the action of them on the vacuum state of the radiation field, superposition of two nonlinear coherent states and two-mode entangled nonlinear coherent states are generated. Also, we show that via the generalization of the presented method, the superposition of more than two nonlinear coherent states and n-mode entangled nonlinear coherent states can be generated.
13 citations
TL;DR: In this article, the authors investigated completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder.
Abstract: We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2, R) group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.
12 citations
TL;DR: In this article, the Perelomov number coherent states for any su(2) Lie algebra were introduced, and the eigenstates of two coupled oscillators were shown to be the SU(2)-Perelomomov coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.
Abstract: From the definition of the standard Perelomov coherent states we introduce the Perelomov number coherent states for any su(2) Lie algebra. With the displacement operator we apply a similarity transformation to the su(2) generators and construct a new set of operators which also close the su(2) Lie algebra, being the Perelomov number coherent states the new basis for its unitary irreducible representation. We apply our results to obtain the energy spectrum, the eigenstates and the partition function of two coupled oscillators. We show that the eigenstates of two coupled oscillators are the SU(2) Perelomov number coherent states of the two-dimensional harmonic oscillator with an appropriate choice of the coherent state parameters.
10 citations
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TL;DR: In this paper, Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box, and a supersymmetric partner system is also presented, as well as a construction of coherent states in this new system.
Abstract: Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in this new system. We show that these states can be chosen, in both systems to have many properties usually expected for coherent states. In particular, they yield highly localised wave packets for a short period of time, which evolve in a quasi-classical manner and which saturate approximately Heisenberg uncertainty relation. These studies are elaborated in one- and two-dimensional contexts. Finally, some relations are established between the gaussian states being mostly used here and the generalised coherent states, which are more standardly found in the literature.
9 citations
TL;DR: In this paper, the authors introduced Holstein-Primakoff representation of α-deformed algebra and achieved the associated non-linear coherent states, including su(2) and su(1, 1, 1) coherent states.
Abstract: In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter
9 citations
TL;DR: A genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.
Abstract: We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems.
The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particlecontributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.
9 citations
TL;DR: In this article, the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice is considered.
Abstract: We consider the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice. These scenarios are currently experimentally feasible. The parameters of the ellipse and the lattice and the coefficients of the constituent coherent states are optimized numerically, via a genetic algorithm, in order to obtain the best approximation. It is found that for certain quantum states the obtained approximation is better than the ones known from the literature thus far.
TL;DR: In this article, a generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed, which is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability.
Abstract: A generalized version of the coupled coherent states method for coherent states of arbitrary Lie groups is developed. In contrast to the original formulation, which is restricted to frozen-Gaussian basis sets, the extended method is suitable for propagating quantum states of systems featuring diversified physical properties, such as spin degrees of freedom or particle indistinguishability. The approach is illustrated with simple models for interacting bosons trapped in double- and triple-well potentials, most adequately described in terms of SU(2) and SU(3) bosonic coherent states, respectively.
01 Sep 2015
TL;DR: In this article, the authors propose to construct nonlinear coherent states for Hamiltonian systems having linear and quadratic terms in the number operator by means of the following two definitions: (i) deformed annihilation operator coherent states and (ii) as deformed displacement operation coherent states (DOCS).
Abstract: On the basis of the f-deformed oscillator formalism, we propose to construct nonlinear coherent states for Hamiltonian systems having linear and quadratic terms in the number operator by means of the following two definitions: (i) as deformed annihilation operator coherent states and (ii) as deformed displacement operator coherent states (DOCS). For the particular cases of the Morse and modified Poschl-Teller potentials, modeled as f-deformed oscillators (both supporting a finite number of bound states), the properties of their corresponding nonlinear coherent states, viewed as DOCS, are analyzed in terms of their occupation number distribution, their evolution on phase space, and their uncertainty relations.
TL;DR: In this paper, shape-invariant trigonometric potentials for the displacement-operator-derived effective mass Hamiltonian were derived by linearizing the algebra resulting from SUSY-QM factorization of the constructed systems.
Abstract: Applying the supersymmetric quantum mechanics approach, we derive shape-invariant trigonometric potentials for the displacement-operator-derived effective mass Hamiltonian. By linearizing the algebra resulting from SUSY-QM factorization of the constructed systems, their coherent states are defined and shown to be exponentially dependent on a function of the quantum numbers.
TL;DR: In this paper, the Fock expansion of pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states, and a relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained.
Abstract: The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampe de Feriet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, as shown for two-mode and three-mode Gaussian states.
TL;DR: In this article, an algebraic formulation for the generalized thermal coherent states with a Thermofield Dynamics approach for multi-modes, based on coset space of Lie groups, was developed.
Abstract: In this paper, we developed an algebraic formulation for the generalized thermal coherent states with a Thermofield Dynamics approach for multi-modes, based on coset space of Lie groups. In particular, we applied our construction on $SU(2)$ and $SU(1,1)$ symmetries and we obtain their thermal coherent states and density operator. We also calculate their thermal quantum Fidelity and thermal Wigner function.
TL;DR: In this article, the photon-added anharmonic oscillators coherent states (PA-AOCSs) were constructed using generalized Heisenberg algebras and the statistical properties of these states were investigated through the Mandel's parameter in terms of the variables involved in the states.
Abstract: In this paper, we construct the photon-added anharmonic oscillators coherent states (PA-AOCSs) using generalized Heisenberg algebras. Klauders minimal set of conditions required to obtain the coherent states are satisfied. The statistical properties of these states are investigated through the Mandel's parameter in terms of the variables involved in the states. It is shown that these coherent states are useful for describing the states of real and ideal lasers in terms of different parameters. These features make these states good candidatures for implementation of schemes in different tasks of quantum optics and information.
TL;DR: In this article, the authors constructed coherent states for anharmonic oscillators using generalized Heisenberg algabras and investigated the statistical properties of these states through the Mandel's parameter and Wehrl entropy.
Abstract: Coherent states for anharmonic oscillators (nonharmonic oscillators) are constructed using generalized Heisenberg algabras. Klauder’s minimal set of conditions required to obtain coherent states are satisfied. The statistical properties of these states are investigated through the Mandel’s parameter and Wehrl entropy. It is shown that these coherent states are useful for describing the states of real and ideal lasers in terms of different parameters.
TL;DR: In this article, generalized coherent states for a family of iso-spectral oscillator Hamiltonians are constructed from a suitable choice of the step operators of the harmonic oscillator, and the non-classical property of these coherent states are investigated.
Abstract: Generalized coherent states for a family of iso-spectral oscillator Hamiltonian are constructed from a suitable choice of the step operators of the harmonic oscillator. We investigate the non-classical property of these coherent states.
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TL;DR: In this article, a brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given, including quantization maps, phase space probability distributions and semiclassical phase spaces.
Abstract: A brief summary of the application of coherent states in the examination of quantum dynamics of cosmological models is given. We discuss quantization maps, phase space probability distributions and semiclassical phase spaces. The implementation of coherent states based on the affine group resolves the hardest singularities, renders self-adjoint Hamiltonians without boundary conditions and provides a completely consistent semi-classical description of the involved quantum dynamics. We consider three examples: the closed Friedmann model, the anisotropic Bianchi Type I model and the deep quantum domain of the Bianchi Type IX model.
TL;DR: In this paper, the authors constructed the unknown Gilmore-Perelomov coherent states for the rotating anharmonic Kratzer-Fues oscillator by applying the algebraic approach and the displacement operator to the ground state.
Abstract: By applying the algebraic approach and the displacement operator to the ground state, the unknown Gilmore–Perelomov coherent states for the rotating anharmonic Kratzer–Fues oscillator are constructed. In order to obtain the displacement operator the ladder operators have been applied. The deduced SU(1, 1) dynamical symmetry group associated with these operators enables us to construct this important class of the coherent states. Several important properties of these states are discussed. It is shown that the coherent states introduced are not orthogonal and form complete basis set in the Hilbert space. We have found that any vector of Hilbert space of the oscillator studied can be expressed in the coherent states basis set. It has been established that the coherent states satisfy the completeness relation. Also, we have proved that these coherent states do not possess temporal stability. The approach presented can be used to construct the coherent states for other anharmonic oscillators. The coherent states proposed can find applications in laser-matter interactions, in particular with regards to laser chemical processing, laser techniques, in micro-machinning and the patterning, coating and modification of chemical material surfaces.